Soft topological hyperstructure

Abstract

Molodtsov proposed the theory of soft sets which can be considered as a recent mathematical tool to deal with uncertainties. The main purpose of this paper is to give the definition of soft topological hypergrupoid by examining the concept of hypergrupoid which is one of the hyperystructures with soft set theory from the topological point of view. Also, the relation between soft topological hypergroupoids and soft hypergroupoids is examined and some theoretical results are obtained. By introducing the concept of soft good topological homomorphism, the category of soft topological hypergrupoids is constructed. At last, the definition of soft topological subhypergrupoid is presented and some related properties are studied.

Soft semi-topological polygroups

“…Samanta under the name Neighbourhood properties of soft topological spaces in [20], also about Soft set theory by P. K. Maji, R. Biswas and A. R. Roy in [15], Soft topological groups and rings by T. Shah and S. Shaheen in [27], On soft topological hypergroups by G. Oguz in [24], On soft topological spaces by M. Shabir and M. Naz in [26]. Only a genius like T. Hida can write such a beautiful story about the Soft topological group in [11], also G. Oguz with article Soft topological hyperstructure in [25] and M. Shabir, M. Naz With their own handwriting about the On soft topological spaces in [26]. If you want to read interesting articles about the topological polygroups, 690 R. MOUSAREZAEI, B. DAVVAZ you can read Heidari's article about the Topological polygroups in [9], also about the Idealistic soft topological hyperrings by G. Oguz in [23] and A new view on topological polygroups by G. Oguz in [22], Soft sets and soft groups by H. Aktas and N. Cagman in [1], Prolegomena of Hypergroup Theory by P. Corsini in [5].…”